In 2D ultrasound Doppler blood flow imaging, the signal power, velocity, and velocity spread are calculated from autocorrelation estimates of the received echo signal in each point of the image, and coded into colors for display. A corresponding technique is referred to as `correlated pulsed pair` in Weather radar applications as discussed in D. S. Zrni'c, "Spectral moment estimates from correlated pulsed pair" IEEE Trans. on Aerosp. Electron., vol. AES-13. pp. 344-354, 1977. It was first applied to ultrasound blood velocity measurement as discussed in C. Kasai, K. Namekawa, A. Koyano, and R. Omoto, "Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique" IEEE Trans. Sonics Ultras., vol. SU-32, pp. 458-464, 1985, under the name `autocorrelation method`. A severe limitation of this technique is the velocity ambiguity problem, which occurs when the Doppler shift frequency exceeds the Nyquist limit at half the repetition frequency of the transmitted pulses. Several methods have been proposed to partly overcome this problem.
Time delay estimation from pulse to pulse by cross correlation technique was applied to ultrasound color flow imaging by Bonnefous as discussed in O. Bonnefous and P. Pesque, "Time domain formulation of Pulse-Doppler Ultrasound and Blood Velocity Estimation by Cross-Correlation" Ultrason. Imaging, vol. 8. pp. 73-85, 1986. This known algorithm operates directly on the received RF (radio frequency) signal, without previous demodulation to baseband.
In U.S. Pat. No. 5,081,994, D. Hassler describes a method applied to the complex demodulated (baseband) signal to avoid aliasing by combining the phase and amplitude of the autocorrelation function.
Hassler uses a simplified algorithm for calculation of the complex correlation function, which gives lower precision (increased variance). In Hassler's method, the correlation phase is calculated by a division followed by inverse tangent. This gives additional ambiguity in the determination of the velocity. In Hassler's method, the correlation phase is not calculated at the lag where the correlation function has its maximum, which gives lower precision for high velocities. Hassler also uses two different approximations for estimating the magnitude of the correlation function, which is different from the mathematical definition. Hassler does not use interpolation in determining the time-shift at peak correlation.
Another approach was used by Ferrara & Algazi as discussed in Ferrara and Algazi, "A new wideband spread target maximum likelihood estimator for blood velocity estimation--Part I: Theory" IEEE Trans. Ultrason. Ferroelec. and Freq. contr., vol. UFFC-38, pp. 1-26, 1991; and Ferrara and Algazi, "The Effect of Frequency Dependent Scattering and Attenuation on the Estimation of Blood Velocity Using Ultrasound" IEEE Trans. Ultrason. Ferroelec. and Freq. contr., vol. UFFC-39, pp. 754-767, 1992. From a stochastic model of the signal from a point scatterer, a maximum likelihood estimate for the velocity was derived, which has the potential to resolve velocity ambiguity. A similar method based on the two-dimensional Fourier transform was proposed by Wilson in K. Miller, Complex Stocastic Processes, Addison-Wesley Publishing Company, Inc., 1974, where a velocity spectrum was obtained by summation along straight lines in the 2D Fourier plane. This method is also described in U.S. Pat. No. 4,930,513, referred to as "radial projection in the 2D Fourier plane".